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Quality-Driven Synthesis of Embedded Multi-Mode Control Systems

Quality-Driven Synthesis of Embedded Multi-Mode Control Systems. Soheil Samii 1 , Petru Eles 1 , Zebo Peng 1 , Anton Cervin 2. 1 Dept. of Computer and Information Science Linköping University Sweden. 2 Dept. of Automatic Control Lund University Sweden. Motivation. Plant. Plant.

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Quality-Driven Synthesis of Embedded Multi-Mode Control Systems

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  1. Quality-Driven Synthesis of Embedded Multi-Mode Control Systems Soheil Samii1, Petru Eles1, Zebo Peng1, Anton Cervin2 1 Dept. of Computer and Information Science Linköping University Sweden 2Dept. of Automatic Control Lund University Sweden

  2. Motivation Plant Plant • Number of modes = 2Numberofcontrol loops • Cannot afford the synthesis time • Cannot store all controllers and schedules Plant Plant

  3. Outline • System model and control performance • Example and problem formulation • Synthesis approach • Experimental results

  4. System model Plant disturbance v(t) Internal-state vector x(t) Plant Output y(t) Input u(t) What is a good sampling period? What is a good control law u? Measurement noise e(t) A/D D/A Controller Linear plant model: • dx(t)/dt = Ax(t) + Bu(t) • y(t) = Cx(t) Linear plant model: • dx(t)/dt = Ax(t) + Bu(t) + v(t) • y(t) = Cx(t) + e(t) Application model: • Periodic tasks • Data dependencies

  5. Control performance • Quadratic cost: J = E{ xTQ1x + uTQ2u } • Depends on • the sampling period, • the control law, and • the schedule (delays between sampling and actuation)

  6. Synthesis of a mode (DATE’09) Scheduling and synthesis tool Minimize Periods Control laws

  7. Example Plant 1 S S C A A C A Plant 2 Plant 3 S C S C A 10 20 30 40 J1 = 3.0 J2 = 1.2 J3 = 2.2

  8. Example Plant 1 Plant 2 Plant 3 S S C A A C A J1 = 3.0 J2 = 1.2 S C S C A 10 20 30 40

  9. Example Plant 1 Plant 2 Plant 3 Previous case: J1 = 3.0 J2 = 1.2 S C A J1 = 1.6 J2 = 1.4 S C A 10 20 22

  10. Example J1 = 3.0 J2 = 1.2 J3 = 2.2 1 1 1 1 2 2 2 2 3 3 3 3 J1 = 1.6 J2 = 1.4 Cumulative cost of all modes: 19.6 J1 = 3.0 J3 = 2.2 J1 = 1.6 J2 = 1.2 J3 = 2.2

  11. Problem formulation • Inputs: • Multi-mode control system (architecture, tasks, plants) • Available memory on each computation node • Outputs: • Schedules and controllers for some modes • Cost to minimize: • Cumulative cost of each functional mode

  12. Some modes are functionally excluded Synthesis approach J1 = 2.5 J2 = 1.5 J4 = 2.0 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 1 J1 = 2.3 J2 = 1.2 Impr. = 12.5% J1 = 2.0 J3 = 2.2 Impr. = 16.0% J1 = 2.0 J4 = 1.2 Impr. = 20.0% J2 = 1.8 J4 = 1.3 Impr. = 11.4% • Synthesis time versus quality • Parameter λ (20% in our example) 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 J1 = 1.2 Impr. = 40% J4 = 1.2 Impr. = 0% Require at least λ = 20% improvement

  13. Synthesis approach Cost = 23 Mem = 18 Cost = 23 Mem = 20 Cost = 19 Mem = 20 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 1 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 • ILP formulation

  14. Synthesis approach 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 1 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4

  15. Experiments – Synthesis Quality Cost improvement [%] λ = 0% λ = 10% λ = 30% λ = 50% Number of control loops

  16. Experiments – Synthesis Time Runtime [seconds] λ = 0% λ = 10% λ = 30% λ = 50% Number of control loops

  17. Summary and Contribution • Two important problems in synthesis of multi-mode control systems • Time complexity (offline) • Memory complexity (online) • Contribution: • Synthesis tool with performance/time/memory trade-off

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